Simplify the following expression: $\sqrt{117}+\sqrt{52}+\sqrt{208}$
First, try to factor any perfect squares out of the radicals. $= \sqrt{117}+\sqrt{52}+\sqrt{208}$ $= \sqrt{9 \cdot 13}+\sqrt{4 \cdot 13}+\sqrt{16 \cdot 13}$ Separate the radicals and simplify. $= \sqrt{9} \cdot \sqrt{13}+\sqrt{4} \cdot \sqrt{13}+\sqrt{16} \cdot \sqrt{13}$ $= 3\sqrt{13}+2\sqrt{13}+4\sqrt{13}$ Finally, simplify by combining the terms. $= ( 3 + 2 + 4 )\sqrt{13} = 9\sqrt{13}$